i looked on myapartmentmap to try and find an apartment that fit your criteria. you didn't specifically mention a price range.

There are options like the Arbors of Brookdale, where 2 bedrooms start at $1200, come with a washer/dryer and storage, one indoor one outdoor pool, a gym, etc. I am not sure if you consider $1200/month pricy for the amenities it offers. If you're interested, their number is (877)333-0994 and they also have a website.

The Courtyards Village is slightly more inexpensive, and a 2 bedroom is around $1030/month. There is a heated swimming pool, and laundry facilities onsite. I don't think utilities are included in this apartment, or the previous I've listed. In any case, their number is (877) 519-6904.

If you would consider living in Aurora, 2 bedrooms start at $1015/month, and there is a washer/dryer in unit, a pool on site, and central air. Their number is (877)359-1612.

The apartment more inexpensive than $1015 a month in a 10 mile radius is at Prentiss Creek in Downers Grove. A 2 bedroom starts at $975/month, and there is a pool/laundry facility onsite. Their number is (630) 426-3192.

Unfortunately, the majority of listings do not specifically include the immediate availability, as it fluctuates more frequently than the ads are updated, which is why I've included the phone numbers. Also unfortunately, I didn't see any listings that said whether they include utilities or not. I'm sorry I couldn't be of much more help, but maybe one of these will give you an idea :)